One of Bertrand Russell's great contributions to rethinking formal logic came from an effort to account for the truth or falsity of a sentence such as "The present king of France is bald." If there is no such person as the present king of France, what would it mean to say that he is bald--or that he is not? His answer (considerably oversimplified from his own statement of it) was to express the sentence hypothetically, as though we are saying "If there is someone such that he is the present king of France, then he is bald."

The notational system used by Russell differs most visibly from the conventional notation in use today in its use of dots for parentheses. Also, in a use that is still very widespread, he relied on the Greek alphabet for his variables. Someone looking today at the three volumes of the book he did with Whitehead (Principia Mathematica) would find it quite difficult to follow Russell's train of thought, but the concepts behind this highly technical work are also developed in his books Principles of Mathematics and Introduction to Mathematical Philosophy.

Russell saw symbolic logic as a tool for the development of pure mathematics, and this is reflected in the rigidly formal approach he takes. Later systems have come to rely more on setting up a package of rules explaining the operations possible with different symbols with a compromise between efficiency (with more symbols and rules) and simplicity (with fewer symbols and rules).

Return to What to Expect.

Return to Implication.

Go back to the starting page.